Class 7 Math Solution WBBSE Geometry Chapter 6 Parallel Lines And Transversal Exercise 6 Solved Problems
Parallel lines:
⇒ If two straight lines on the same plane do not intersect when produced in any direction, the two straight lines are said to be parallel to one another.
⇒ In the adjacent image, the straight lines AB, CD, and EF are parallel to each other i.e., AB || CD || EF
Transversal:
⇒ If a straight line intersects two or more straight lines in different points then the straight line is called a transversal of the lines.
⇒ In the adjacent image, the straight line EF intersects the straight lines AB and CD at points G and H respectively. So EF is called the transversal of lines AB and CD.
Vertically opposite angles:
⇒ If two straight lines intersect at a point, the angles formed on the opposite sides of the common point (vertex) are called vertically opposite angles.
⇒ In the adjacent image, two straight lines AB and CD intersect at O. ∠AOC and ∠BOD are two vertically opposite angles. Also, ∠AOD and ∠BOC are two vertically opposite angles.
Interior angles and exterior angles:
⇒ In the adjacent image ∠3, ∠4, ∠5, and ∠6 are interior angles whereas ∠1, ∠2, ∠7, and ∠8 are exterior angles.”
Corresponding angles:
⇒ Two angles lying on the same side of the transversal are known as corresponding angles if both lie either above are below the two given lines.
Alternate angles:
⇒ The pair of interior angles on the opposite side of the transversal are called alternate angles.
⇒ In the adjacent image, there are four pairs of corresponding angles. (∠1, ∠5), (∠2, ∠6), (∠8, ∠4), and (∠7, ∠3). There are two pairs of alternate angles (∠4,∠6) and (∠3, ∠5).
⇒ If a straight line intersects two parallel lines then the measurement of each pair of corresponding angles are equal and the measurement of alternate angles are equal.
⇒ Hence, ∠AGE = ∠GHC, ∠CHF = ∠AGH, ∠DHF = ∠BGH and ∠EGB = ∠GHD
⇒ Again, ∠AGH = ∠GHD and ∠BGH = ∠GHC
⇒ [The sum of the measurement of two interior angles in the same side of the transversal is 180°]
WB Class 7 Math Solution Parallel Lines And Transversal
Parallel Lines And Transversal Exercise 6
⇔ When the lines not parallel
⇔When the lines are parallel
⇔Lines are not parallel:
⇔Lines are parallel:
